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Modeling and Measuring Ferry Boat Wake Propagation

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Modeling and Measuring Ferry Boat Wake Propagation 1 MODELING AND MEASURING FERRY BOAT WAKE 2 PROPAGATION 1 3 Brad Perfect Dr. Jim Thomson 2 Dr. James Riley 3 4 ABSTRACT 5 Surface waves generated by vessels were studied for two classes of ferries in the 6 Washington State Department of Transportation (WSDOT) system. The vessel 7 wakes were measured using a suite of free-drifting GPS buoys. The wakes were 8 modeled using an analytical potential flow model, which has a strong dependence 9 on vessel Froude number and vessel aspect ratio. Both the measurements and 10 the model are phase-resolving, and thus direct comparisons are made, in addition 11 to comparing bulk parameters. The model has high fidelity for the parameters 12 describing the operating conditions for WSDOT vessels, successfully reproducing 13 the measured difference between the two vessel classes and the dependence on 14 vessel speed for each vessel class. 15 Keywords: Free Surface, Ship Wake, Kelvin Wake. 1PhD Student, Dept. of Mechanical Engineering. Univ. of Washington. 3900 Stevens Way NE, Seattle, WA 98195. E-mail: [email protected]. 2Principal Oceanographer, Applied Physics Laboratory. Univ. of Washington. 1013 NE 40th St, Box 355640, Seattle, WA 98105. E-mail: [email protected] 3PACCAR Prof. of Engr., Dept. of Mechanical Engineering. Univ. of Washington. 3900 Stevens Way NE, Seattle, WA 98195. E-mail: [email protected] 1 16 INTRODUCTION 17 Washington State Ferries (WSF) operates a fleet of 22 vessels in the Puget 18 Sound region of Washington State, USA, and British Columbia, Canada. It is 19 the largest ferry system in the United States and services the highest volume 20 of automobiles of any ferry service in the world. The Seattle-Bremerton route, 21 servicing 2.33 million passengers and 642,000 vehicles per year (Smith 2013), is 22 the primary subject of the current study. In a section of this route named Rich 23 Passage, denoted by the box in Fig. ??, the channel narrows to 600m (?). Due 24 to the narrow channel and steep bathymetry of the region, vessel wake-induced 25 erosion is a concern for the surrounding shoreline. 26 A vessel operating protocol (power limit) of 8.2 m/s (16 knots) is presently 27 in place to reduce wake-induced morphological effects within the channel (Klann 28 2002). The WSF vessels that serve the Seattle-Bremerton route are known as 29 Issaquah Class and Super Class vessels. While of qualitatively similar size, the 30 Super Class vessels are longer, narrower, and heavier than the Issaquah Class 31 vessels. The protocol is applied to the Issaquah Class only, because the Issaquah 32 Class wakes have been classified, visually, as much larger than the Super Class 33 wakes. This paper seeks to quantify the differences between the wakes of the two 34 vessel classes through the use of field data and an analytical model. 35 Rich Passage has been the subject of a comprehensive wake and shoreline 36 study conducted upon the introduction of the Rich Passage I, a passenger-only 37 fast ferry that served the Seattle-Bremerton route for Kitsap Transit. The study, 38 conducted by Golder and Associates, concluded that the Rich Passage I meets 39 wake height guidelines specified by 8 > <>H < 0:2 T ≤ 3:5 40 H = (1) > −1:4 :>H < 1:16T T > 3:5 2 41 where H is the the wake height in meters measured 300m from the sailing line of 42 the vessel, and T is the wake period in seconds. This criterion is based on the 43 observation that low-frequency waves contain more erosive potential because of 44 their higher energy flux, and therefore have a more restrictive associated height 45 limit. The morphological shoreline response was largely inconclusive (Cote et al. 46 2013). 47 WSF commissioned a similar study of the car ferry fleet in 1985 to measure 48 vessel wakes (Nece et al. 1985). This study involved Issaquah, Superclass, and 49 Evergreen class models in open water in Puget Sound. No modeling efforts ac- 50 companied this study, and no curve fitting or statistical analysis were performed. 51 The results establish qualitatively that the Super class vessel wakes grow at a 52 much slower rate as vessel speed increases when compared to the Issaquah class. 53 However, noise in wake data and difficulties in establishing the buoy-boat dis- 54 tance make the conclusions difficult to quantify. Despite these shortcomings, it 55 was found that the data from this study could be used to supplement the field 56 data from the current study. Uncertainty in wake height due to natural varia- 57 tion in time-dependent surface wave conditions dominated uncertainty due to the 58 buoy-boat distances. 59 The more general objective of predicting boat wakes has generally been ap- 60 proached as either a computational fluids problem, or as an empirical quantifi- 61 cation of wave height. Previous modeling efforts of phase resolved vessel wakes 62 have been confined to domains of only a few boat lengths due to computational 63 requirements (Raven 1998), which provide limited information about potential 64 shoreline impact. Sophisticated near-vessel models are primarily used to model 65 wave breaking and wave making resistance for naval architectural applications 66 (Landrini et al. 1999; Huang and Yang 2016). Phase-averaged models have been 67 successfully implemented (Cote et al. 2013), but the resultant wake structure 3 68 is lost. Other phase-resolved models have focused on vessels with transcritical 69 Froude numbers in shallow water (Kofoed-Hansen et al. 1999). Empirical models 70 have been used to great success within the bounds of the space sampled (Sorensen 71 1997; Kriebel et al. 2003; Ng and Bires ) 72 The analytic study of ship wakes was first considered mathematically in 1887, 73 when Lord Kelvin showed that the disturbance caused by a point pressure source 74 moving across a fluid surface forms a predictable structure which now bears his 75 name (Thomson 1887). Subsequent work focused on the geometry and structure of 76 wakes, with extensions for arbitrary motion of the pressure point (Stoker 1957). 77 Significant gains have been made more recently, with results detailing surface 78 velocity fields (Yun-gang and Ming-de 2006), the inclusion of viscous forces (Lu 79 and Chwang 2007), and finite vessel dimensions (Darmon et al. 2014; Benzaquen 80 et al. 2014). 81 The impact of boat wakes on shoreline, and mitigation thereof, has been a 82 continuous concern for caretakers of waterways, as well as a subject of many 83 previous studies (Glamore 2008; Aage et al. 2003; Verhey and Bogaerts 1989). In 84 particular, work has been done on the sediment transport associated with vessel- 85 generated waves (Velegrakis et al. 2007). 86 The effects of bow wakes, which are known to have complex hull-dependent 87 forms (Noblesse et al. 2013) are not considered in this study, though results suggest 88 that they may dominate the vessel-generate wave field for low Froude number. 89 METHODS 90 Analytical Model 91 The first analytic study of wake patterns was published in 1887, when Lord 92 Kelvin showed that the disturbance caused by a point pressure source moving 93 across a fluid surface forms a predictable structure which now bears his name 94 (Thomson 1887). Subsequent work focused on the geometry and structure of 4 95 wakes, with extensions for arbitrary motion of the pressure point (Stoker 1957). 96 A closed form expression for the sea surface height caused by a finite pressure 97 distribution moving across a fluid surface was recently developed (Benzaquen et al. 98 2014; Darmon et al. 2014). The equations developed by Darmon, Benzaquen, et 99 al. are the basis for the analytical modeling presented below. 100 The analytical model must be confined to potential flow theory in order to 101 yield tenable solutions for the sea surface height. Therefore, the restrictions 102 µ = 0 and ~! = r × ~u = 0; (2) 103 are required. Here, µ is the viscosity of the flow, ~u is the flow field in Euclidean 104 coordinate space, and ~! is the vorticity. 105 The sea surface height generated by a moving pressure distribution p(x; y) 106 (Rapha¨eland deGennes 1996) is given by Z 1 Z 1 −i(kxx+kyy) dkxdky kp^(kx; ky)e 107 ζ(x; y) = − lim 2 2 2 2 (3) !0 0 0 4π ρ !(k) − U kx + 2iUkx 108 wherep ^(kx; ky) is the Fourier transform of the pressure distribution p(x; y), ρ is the p 2 2 109 constant fluid density, !(k) is the surface wave dispersion relation, k = kx + ky, 110 and U is the pressure distribution's constant forward velocity. The parameter is a −1 111 variable with units s that approaches zero, ensuring that the radiation boundary 112 condition is satisfied. For a derivation of Eq. (3), the reader is referred to Rapha¨el 113 and deGennes (1996). Define a coordinate system such that the vessel is located 114 at the origin, and is moving in the −x-direction, with the sea surface displacement 115 in the z-direction. The y-axis defines the neutral sea surface perpendicular to the 116 sailing line of the vessel. Following the method developed by Darmon et al., the 5 117 nondimensionalization conditions for a boat of length b are: x y X = Y = K = k b b b X x s (4) 118 4π2ζ p^ b K = k b Z = P^ = ~ = ; Y y b ρgb3 g 119 Nondimensionalization yields Z(X; Y )b Z π=2 Z 1 dK dK K ρgb3P^(K ;K )e−i(KX X+KY Y ) = − lim X Y b x y 2 2 2 gK K2 g K 4π ~!0 −π=2 0 4π b ρ 2 X p X b − U b2 + 2i~ b U b Z π=2 Z 1 3 ^ −i(KX X+KY Y ) dKX dKY Kρgb P (Kx;Ky)e 120 Z(X; Y ) = − lim (5) 4 gK K2 g ~!0 −π=2 0 b ρ 2 X p b − U b2 + 2i~ b3 UKX Z π=2 Z 1 dK dK KP^(K ;K )e−i(KX X+KY Y ) = − lim X Y x y ~!0 2 2 −π=2 0 K − F r KX + 2iF~ rKX 121 An elliptic transform ˘ ˘ ˘ ˘ −1 ˘ ˘ 122 X = R cos'Y ˘ = W R sin'K ˘ X = K cos θ KY = W K sin θ; (6) 123 permits solutions for an elliptic Gaussian pressure distribution.
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